Modeling of Transient Heat Flux in Spark Ignition Engineduring Combustion and Comparisons with Experiment

Modeling of Transient Heat Flux in Spark Ignition EngineDuring Combustion and Comparisons with Experiment

Yusaf T.F., Sye Hoe, Fong, Yusoff M.Z. and Hussein I. Universiti Tenaga Nasional, Department of Mechanical Engineering, Km 7, Jalan Kajang-Puchong Kajang, Selangor 43009, Malaysia

Abstract: A quasi-one dimensional engine cycle simulation program was developed to predict the transient heat flux during combustion in a spark ignition engine. A two-zone heat release model was utilized to model the combustion process inside the combustion chamber. The fuel, air and burned gas properties throughout the engine cycle were calculated using variable specific heats. The transient heat flux inside the combustion chamber due to the change in the in-cylinder gas temperature and pressure during combustion was determined using the Woschni heat transfer model. The program was written in MATLAB together with the Graphical User Interface (GUI). Numerical results were compared with the experimental measurements and good agreement was obtained. Four thermocouples were used and positioned equi-spaced at 5mm intervals along a ray from the spark plug location on the engine head. These thermocouples were able to capture the heat flux release by the burned gas to the wall during the combustion process including the cycle-to-cycle variations. Pressure sensor was installed at the engine head to capture the pressure change throughout the cycle.

Key words: Internal combustion engine, Woschni, spark ignition engine, heat flux, mathematical model

INTRODUCTION for both burned and unburned gases were expressed as functions of temperatures as follows: Heat transfer between the working fluid and the & (2) Qb = hAb (Tb − Tw ) combustion chamber in the internal combustion engine Q& = hA (T − T ) (3) is one of the most important parameter for cycle u u u w Where, and are the areas of the burned and simulation and analysis. Heat transfer influences the in- Ab Au cylinder pressure and temperature levels, engine unburned gas in contact with the cylinder walls at efficiency and exhaust emissions. During the temperature . The wall temperature is assumed to be Tw combustion process, the peak gas temperature was 450K which is maximum allowable limit for the limited to 2500K as metal components of the lubricant oil to work under a proper condition before it combustion chamber can only withstand 600K for cast oxidize due to overheat. The cylinder area inside the iron and 500K for aluminium alloys. Therefore, the combustion chamber is: cooling of the cylinder head, block and piston is very πb2 4V  important to keep the engine running in optimum   1/ 2 (4) Ab =  + x condition. The engine lubricant will oxidize if the  2 b  temperature reaches more than 450K. Thus, Likewise for unburned gas investigating the transient heat flux in the cylinder is  πb2 4V  A =  + 1− x1 / 2 (5) very significant. The quasi one dimensional model was u  2 b  acceptable since the temperature gradient normal to the   wall is large compared with the temperature gradients Equation (4) and (5) are empirical functions that along the wall[1]. have the correct limits in the case of a cylinder where and when . The x value represents the mass x → 0 x →1 fraction of cylinder content and burned gas is always Numerical analysis: In order to determine the transient assumed to occupy this larger fraction of the cylinder as heat flux inside the combustion chamber during the compared to unburned gas, due to the density difference combustion process, the heat transfer need to be defined [2] between burned and unburned gas. The burned gas as a function of θ as shown in the following equation : always occupies larger volume fraction of the cylinder. dQ − Q& − Q& − Q& = l = b u (1) Equation (2) and (3) represent the remaining parameter, dθ ω ω that required to determine the heat transfer coefficients. The combustion gases are defined into two zones In the present work, the heat transfer coefficients are which are unburned gas zone and burned gas zone evaluated using Woschni heat transfer model[3]. where & and & are the heat transfer rates for the Qb Qu −0.2 0.8 0.8 −0.55 (6) burned and unburned gas respectively. The heat fluxes hc = 3.26B p w T

Corresponding Author: Yusaf T. F., Universiti Tenaga Nasional, Department of Mechanical Engineering, Km 7, Jalan Kajang-Puchong, Kajang, Selangor 43009, Malaysia 1438 Am. J. Applied Sci., 2 (10):1438-1444, 2005

Where: temperature combustion modelling. The internal b = bore energy, enthalpy and specific heats are function of p = pressure pressure and temperature. On the other hand, in the T = temperature burned routine, ten combustion species were tracked w =average cylinder gas velocity during the combustion process using chemical equilibrium combustion model. Both of these routines The average gas velocity is always assumed to be return partial derivatives in logarithmic form, which are required in the subsequent calculations. The specific proportional to the mean piston speed during the intake, [2] compression and exhaust stroke. However, during the internal energy of the system is given U (10) combustion process, the gas velocity is a function of u = = xub + ()1− x uu density due to temperature and pressure rise. Thus, the m average gas velocity is Since there are two combustion zones inside the cylinder, x represents the mass fraction of the burned V T  w = C S + C d r ()P − P (7) gas, is the internal energy of the burned gas at 1 p 2   m ub  PrVr  temperature T and u is the internal energy of the Where: b u = piston displacement unburned gas at temperatureT . The internal energy of Vd u S = mean piston speed the burned gas is function of both temperature and p pressure. = reference temperature Tr (11) ub = ub (Tb , P) p ,V = pressure and volume at initial condition r r and the derivatives will be = motored pressure pm du ∂u dT ∂u dP b = b b + b (12) C1 = 2.28, C2 = 0.0 during the compression stroke dθ ∂Tb dθ ∂P dθ C = 2.28, C = 0.00324 during the combustion and by substituting the logarithmic form of partial 1 2 [2] expansion stroke derivatives return by the burned routine du  Pv ∂lnv  dT  ∂lnv ∂lnv  dP b  b b  b  b b  (13) = cPb −  − vb  +  In order to determine the average gas velocity, the dθ  Tb ∂lnTb  dθ  ∂lnTb ∂ln P  dθ pressure and temperature histories throughout the cycle and for the unburned gases are required. Both of these parameters are functions of duu  Pvu ∂lnvu  dTu  ∂lnvu ∂lnvu  dP (14) thermodynamic properties. Based on the first law of = cPu −  − vu  +  [2] dθ  T ∂lnT  dθ  ∂lnT ∂ln P  dθ thermodynamics ,  u u   u  ∆U = Q −W (8) Equation (10) can be expressed in derivatives form as Where, the change of internal energy of any system follows, is equal to the difference between the heat transfer and du  dub duu dx  (15) m = x + ()1− x + ()ub − uu m work generated by the system. The above equation can dθ  dθ dθ dθ  be expressed in differential form and when applied to a Substituting equations (13) and (14) into equation (15), control volume encasing the cylinder content, the du PvvdTbbb∂ln mmxc= Pb −+ equation becomes: dTTdθ bb∂ln θ (16) du dm dQ dV m&1h1 Pv∂ ln v dT m + u = − P − (9) uuu mxc()1−−Pu dθ dθ dθ dθ ω TTduu∂ ln θ Where:    ∂ln vb ∂ lnvb   ∂ln vu ∂ ln vu  dP − mxvb  +  + m()1− x vu  +  m&1 = mass flow rate       ∂lnTb ∂ln P   ∂lnTu ∂ln P  dθ = enthalpy of the blowby masses h1 dx + m()u − u u = internal energy b u dθ Q = heat transfer This equation defined the first term on the left hand side p = pressure of equation (9).

V = volume Specific volume: The specific volume of the system = crank angle θ can be expressed in a similar manner as the specific = engine speed [2] ω internal energy

U (17) Thermodynamic properties v = = xvb + ()1− x vu m Specific internal energy: Since the thermodynamic and the function form will be properties change with respect to temperature and v = v T , P (18) pressure, two MATLAB subroutines were programmed b b ( b ) to return the thermodynamic properties throughout the The derivatives is dv ∂v dT ∂v dP engine cycle. The unburned routine was used to b = b b + b (19) calculate the fuel-air-residual gas mixture using low dθ ∂Tb dθ ∂P dθ 1439 Am. J. Applied Sci., 2 (10):1438-1444, 2005 by substituting the logarithmic form partial derivatives specific heat calculation and the specific heat is return by the burned routine assumed to follow a polynomial equation as follows[3]: dv v ∂ ln v dT v ∂ ln v dP C b b b b b b (20) p 2 3 4 (30) = + =a1+a2T + a3T + a4T + a5T dθ Tb ∂ lnTb dθ P ∂ ln P dθ R and for the unburned gas Where, R is the gas constant and a is the curve dvu vu ∂lnvu dTu vu ∂lnvu dP (21) fitted polynomials coefficients. Thus, since ∂h  , = +   = C p dθ Tu ∂ lnTu dθ P ∂ ln P dθ  ∂T  p Likewise, equation (17) becomes by varying the constant specific heat throughout the 1 dV V dm dv dv dx cycle, the enthalpy will change accordingly. − = x b + ()1− x u + ()v − v (22) m dθ m 2 dθ dθ dθ b u dθ Substituting equations (20) and (21) into equation (22) Mass blowby pass rings: The rate of change of mass yields with respect to crank angle is represented in equation 1 dV VC v ∂ lnv dT v ∂ lnv dT (9). By considering the mass conservation equation and + = x b b b + ()1− x u u u (23) m dθ mω T ∂ lnT dθ T ∂ lnT dθ considering the mass lost due to the blowby past the b b u u piston rings, the rate of change of mass with respect to  v ∂ lnv v ∂lnv  dP dx [2] b b u u crank angle can be written as follows : + x + ()1− x  + ()vb − vu  P ∂ ln Pb P ∂ ln Pb  dθ dθ dm − m& − Cm = = (31) dθ ω ω Entropy: The entropy was expressed in a functional Where, ω is the engine rotational speed and the [2] form where constant C is dependent on the ring design inside the (24) su = su ()Tu , P engine. If the total mass loss is assumed to be 2.5%, the and the derivatives is: coefficient is 0.8. dsu  ∂su  dTu  ∂su  dP (25) =   +   Burn fraction, mass and volume of the system: The dθ  ∂T  dθ ∂P dθ  u    burn fraction was expressed in three different phases, Substituting the logarithmic form partial derivatives compression, combustion and expansion[3]. return by the unburned routine yields Before the ignition/compression, ds  C p  dT v ∂ ln v dP u  u  u u u (26) =   − dθ  Tu  dθ Tu ∂ lnTu dθ x = 0 (32) The entropy of unburned gas was taken into During the combustion,   account since the unburned gas was treat as an open 1 πθ −θ s  (33) system losing mass due to leakage and during x = 1− cos  2   θb  combustion process. Moreover, the compression stroke After the combustion/expansion, is no longer defined as isentropic compression.

(34) Enthalpy: During the process of engine running, some x = 1 Were,θ is the spark timing and is the burn of the mass will be lost due to blowby past the piston s θ b rings. This loss in mass will cause enthalpy losses well duration. The mass at any crank angle is assumed to be and will decrease engine performance. Before the given by (35) combustion process, unburned gas leaks past the piston m = m1 exp[− C(θ −θ1 )/ω] rings and after the combustion process, the burned gas Where, m1 is the mass at the start of the also leaks past the piston rings. These losses need to be compression stroke assumed to be 180° before top dead taken in account in the calculation in order to obtain centre (BTDC) and θ1 is 180° BTDC. The cylinder accurate result. In order to relate the enthalpy loss volume is given by: between unburned and burned gases, mass fraction is 1/ 2 [2]   2   used to represent the composition as follows , V 1 1  l  l  2  (36) = +  +1− cosθ −   − sin θ   V r −1 2 a  a  d     h = 1− x2 h + x2h (27) l ( ) u b Where, r is the compression ratio, ε is stroke to Likewise the enthalpy can be written in a function form rod length ratio  s  and V is volume at top dead h = h T , P (28)   d b b ()b  2l  and for unburned gas centre. (29) hu = hu ()Tu , P The specific enthalpies for both burned and Solution procedure: It can be seen from equation (9) unburned gases were computed by the subroutines that all terms had been investigated and the only term burned and unburned and return the values for the left is the work term. The work done by the piston is further calculations throughout the engine cycle. As equal to the product of pressure and the volume change mentioned earlier, this program utilized a variable with respect to crank angle. Solving the last term will 1440 Am. J. Applied Sci., 2 (10):1438-1444, 2005 give the output of pressure, temperature of burned gas, Where: temperature of unburned gas, work done, heat loss and 1  dV VC  (51) [2] A =  +  the enthalpy loss change with respect to crank angle . m  dθ ω  dP (37) 2 = f1()θ , P,Tb ,Tu  πb 4V  dθ  +   2 b  vb ∂lnvb 1 / 2 Tb − Tw dTb (38) B = h ( x = f 2 ()θ, P,Tb ,Tu ωm c ∂lnT T dθ Pb b b dTu vu ∂ ln vu 1/ 2 Tu − Tw (52) = f ()θ , P,T ,T (39) + ()1− x ) dθ 3 b u c ∂ lnT T Pu u u Since the work done, heat loss and enthalpy are dx ∂ ln v h − h  dx ()x − x2 C  related to the pressure, temperature of burned gas and C = −()v − v − v b u b − (53) b u dθ b ∂ lnT c T dθ ω  unburned gas, simultaneous integration of all the above b Pb b   equations will give the pressure, temperature of burned  2 2  vb  ∂ ln vb  vb ∂ ln vb (54) gas, temperature of unburned gas, work done, heat loss D = x   +  c T ∂ lnT P ∂ ln P  and the enthalpy loss change throughout the engine  Pb b  b   cycle.  2 2  vu  ∂ ln vu  vu ∂ ln vu (55) dW (40) E = ()1− x    +  = f 4 ()θ , P cP Tu  ∂ lnTu  P ∂ ln P  dθ  u  dQ Equation (45) and (46) are the main focus of this l = f ()θ , P,T ,T (41) dθ 5 b u study. Both pressure and burned temperature history was used to calculate the heat transfer coefficient by dH l (42) = f 6 ()θ , P,Tb ,Tu using Woschni model and compare with the dθ However, in order to solve the equations above, experimental results. To simulate the engine cycle, another equation need to be derived based on the some parameter was taken from the engine geometry thermodynamic properties. The unburned gas was such as bore, stroke and compression ratio. The air fuel treating as an open system losing heat (Q) due to the ratio at 2180rpm, spark timing and initial pressure are mass transfer and the irreversibility such as mixing: taken from the experiment as the input data for the simulation. ds − Q& = ωm()1− x T u (43) u u dθ Substituting equation (26) into equation (43) to eliminate dsu gives dθ πb2 4V  − h +    1/ 2 dTu ∂ lnvu dP 2 b ()1− x (44) c − v =   ()T −T pu u u w dθ ∂ lnTu dθ ωm ()1− x Thus, equation (9), (23) and (44) yields the solutions for equation (37), (38) and (39). The six equations are then integrated by using the ode45 function in MATLAB. The ode45 uses the Runge-Kutta integration to integrate the ODEs[2]. dP A + B + C = (45) dθ D + E Fig. 1: Pressure history throughout the engine cycle πb2 4V    1 / 2 − h + x ()Tu −Tw dTb  2 b  vb ∂lnvb  A + B + C  = +   dθ ωmc x c ∂lnT D + E Pb Pb b   h − h  dx C  + u b − ()x − x2 (46) xc dθ ω  Pb   πb2 4V  − h + ()1− x1/ 2 ()T − T   u w (47) dTu  2 b  vu ∂lnvu  A + B + C  = +   dθ ωmc ()1− x c ∂lnT D + E Pu Pu u   dW dV = P (48) dθ dθ dQ h πb2 4V  l   1/ 2 1/ 2 (49) =  + []x ()Tb − Tu + ()1− x ()Tu − Tw dθ ω  2 b  Fig. 2: Temperature history throughout the engine dH Cm l = []()1− x2 h + x2h (50) cycle dθ ω u b 1441 Am. J. Applied Sci., 2 (10):1438-1444, 2005

The simulation was developed under no-load operating Coaxial surface junction K-type thermocouple was conditions. The pressure change from compression constructed “in-house” by University of Southern stroke to expansion was clearly shown in Fig. 1 Queensland as described[5] and used for temperature whereas the unburned and burned gas temperature was measurement. The thermocouple junctions were shown in Fig. 2. Both pressure and temperature history constructed by using 120 abrasive grit where based on was very useful parameter to determine the heat flux of previous calibration work, the 120 grit or finer gives the engine cycle. The unburned gas temperature was faster response less than 1µs. These thermocouples usually referred to the residual gas whereby the burned were installed at the engine head with epoxy which gas temperature was referring to the gaseous burning serves as an electrical insulator for the thermocouples. during the combustion. In order to determine the fluctuations in heat flux from the transient surface junction thermocouple Experimental investigation measurements, the “thermal product” needs to be Engine test bed: The engine used for this investigation known. The “thermal product was defined as ρck at the laboratories of University of Southern where ρ is the density, c is the specific heat and k is Queensland was a single cylinder four stroke Briggs and Stratton, model 92232, type 1245E1, 3.5hp vertical the thermal conductivity. From the previous calibration shaft, bore 65mm, stroke 44mm, compression ratio 6 work, the effective thermal product of the gauges was 2 1/ 2 and displacement volume of 146cm3. The main taken as 9000J / m Ks . The signals from bearings are oil lubricated and the engine is air-cooled. thermocouples were amplified with a gain of 500 and then conditioned using electrical analogue units as To avoid the rotating magnetic field by the magneto [6] ignition system interfering with the heat flux described . The voltage signal from this analogue measurement, the ignition system was replaced with an units, pressure transducer and the crank angle encoder electronic system. The pressure transducer and heat flux were recorded using two digital oscilloscopes gauges were install at the cylinder head as shown in (Tektronix TDS420A). Each signal was recorded at Fig. 3. The wires were passed through a hole drilled either 100kSamples/s or 5kSamples/s with a total of through the cylinder head and connected to the charge 30k samples for each signal. The in-cylinder pressure amplifier before it goes to the data acquisition system. was measured by a commercial quartz pressure The engine was operated at approximately 2180rpm transducer (PCB mode number 112B11) and an inline without any loading apart from frictional losses and charge amplifier (PCB model number 402A03) was windage. A once per revolution signal from an infrared used. The pressure transducer was set to have a shaft encoder was used to identify the engine speed. sensitivity of 0.153mV/kPA for temperature lower than The spark timing was also set relative to the signal from 300ºC. the shaft encoder, which is 10.7º BTC[4]. Experimental results

a) Pressure-cycle 1-5

Fig. 3: Illustration of the pressure transducer and thermocouple locations b) Heat flux-cycle 1

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it placed just beside the spark plug. Figure 4b shows the significant rises of heat flux of TC1 and TC2 whereas TC3 and TC4 have significant decay of it. The pressure of each consecutive cycle appears to be similar where Fig. 4a shows the pressure as a change relative to the lowest value measure in the cycle. The peak pressure difference was about 350kPa, which is relatively low.

RESULTS AND DISCUSSION

The mathematical model was developed based on the variation of thermodynamic properties calculations. c) Heat flux-cycle 2 The thermodynamic properties that used in this model were put in empirical function ,where x value represents the mass fraction of the burnt cylinder content. Practically, x has left as a parameter to be determined from experiments, otherwise more complicated scheme may be used based on the assumption of the flame shape. Since the mass fraction differentiate the burned and unburned gas region, the value of x has a significant effect on the accuracy of the results. The temperature history that obtained from the simulation was use in equation (2) and (3) in order to determine the heat flux of unburned and burned gas d) Heat flux-cycle 3 regions. In this case, the burned gas region was only used to be compared with the experimental result since the heat flux was recorded during the combustion phase only. The simulation was in one dimensional and this is acceptable due to the gradient normal to the wall is large compare with the temperature gradient along the wall. Moreover, the temperature differences along the wall decay rapidly since the epoxy seal serves as an insulator to the thermocouple body. A 100 of consecutive heat flux cycles during combustion was simulated and plotted to be compared with the experimental data. In order to obtain closed practical results, engine specifications such as bore, stroke, spark e) Heat flux-cycle 4 timing, rpm, compression ratio and ignition timing should be used as an input data for this mathematical model. The experimental heat flux was found to be slightly lower than numerical one.

Heat Flux Vs. Crank angle @ Combustion phase

0.3 Numerical result 0.25 Experimental result 0.2

0.15 f) Heat flux-cycle 5 0.1 0.05 Fig. 4: a-f: Pressure and heat flux from 5 consecutive Heat flux (MW/m^2) cycles[6] 0 0 50 100 150 200 Figure 4b, c, d, e and f show the heat flux cycle of Crank angle (deg) each thermocouple. The arrow sign indicated the cold structure occurred during the combustion. The heat flux was recorded by TC1 before TC2, TC3 and TC4 since Fig. 5: Heat flux vs. crank angle 1443 Am. J. Applied Sci., 2 (10):1438-1444, 2005

The heat flux losses can be consider zero as the ACKNOWLEDGMENTS calculation considered the flam as adiabatic flame Nevertheless, the trend of the graph is still similar to the The author would like to thank Dr. Buttsworth experimental results. The pressure and heat flux do not from the University of Southern Queensland for increase significantly during combustion the rate of the providing the experimental data. heat release due to combustion is slow, also the volume increases rapidly at he same time. REFERENCES Figure 5 shows the average heat flux cycles of the burned gas during the combustion and the expansion, 1. Oude Nijeweme, D.J., J.B.W. Kok, C.R. Stone and however compression stroke has not considered in this L. Wyszynski, 2001. Unsteady in-cylinder heat case. This is to match with the experimental result from transfer in a spark ignition engine: Experiments University of Southern Queensland that was presented and modelling. Proc. Instn Mech. Engrs. Part D, J. for the burned gas region only[4]. Automobile Engg., 215: 747-760. CONCLUSION 2. Colin R. Ferguson, 1986. Internal Combustion Engines- Applied Thermo Sciences. John Willey & The mathematical model was proven very good Sons. agreement with the experimental results in term of heat 3. John B. Heywood, 2003. Internal Combustion flux and pressure raise during combustion stroke. It was Engine Fundamentals. McGraw-Hill, pp: 371-470. found that the trend of the heat flux curve for both 4. David, R. Buttsworth and C. Matthew Wright, result are having the same paten. The difference 2004. Observations of combustion in a spark between the numerical and experimental result was due ignition engine using transient heat flux to the theoretical assumptions of mass fraction for measurements. 7th Aus. Heat and Mass Transfer burned and unburned gas region. Moreover, the Conf. temperature gradient along the wall was ignored since 5. Buttsworth, D.R. and P.A. Jacobs, 1998. Total the mathematical model was one dimensional model. temperature measurements in a shock tunnel Although the temperature gradient is not that significant facility. 13th Aus. Fluid Mechanics Conf., 1: but still it can causes minor difference from the 51-54. experimental outcome. This model can significantly 6. Oldfield, M.L.G., H.J. Burd and N.G. Doe, 1982. contribute to play very significant role to determine the net heat flux inside the combustion chamber for Design of wide-bandwidth analogue circuits for different type of gaseous fuel. Application wise, the heat transfer instrumentation in transient wind model can be very helpful tool to investigate the quality tunnels.16th Symp. Intl. Centre for Heat and Mass of combustion in the combustion chamber. Transfer, pp: 238-258.

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